Opuscula Math. 39, no. 1 (2019), 49-60
Boundary value problems with solutions in convex sets
Peer Chr. Kunstmann
Abstract. By means of the continuation method for contractions we prove the existence of solutions of Dirichlet boundary value problems in convex sets. As an application we prove the existence of concave solutions of certain boundary value problems in ordered Banach spaces.
Keywords: Dirichlet boundary value problems, solutions in convex sets, continuation method, ordered Banach spaces, concave solutions.
Mathematics Subject Classification: 34B15, 47H10.